Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Solve the following problems.
1. Find two numbers whose product is 64, and whose sum is a minimum.
2. The sum of two numbers is 60. The product of one by the cube of the other is to be a maximum. What are the numbers?
3. The sum of two numbers is 10. Find the numbers if the sum of their squares is to be minimum given that one number is
twice the other.
4. A long strip of tin 30 cm wide is to be made into a gutter with rectangular cross section by turning up equal widths along
the edges. Find the depth of the gutter which yields the greatest carrying capacity.
5. The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the material used to make
the box is a minimum.
6. A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to one of the sides. Find the
dimensions of the largest field that can be enclosed with 8o0 feet of fencing.
7. Find the maximum area of a rectangle inscribed in a semicircle of radius 5 inches if its base lies along the diameter of of
the semicircle.
8. Find the dimensions of the right circular cylinder of maximum volume that can be inscribed in a right circular cone
whose radius is 3 in and whose height is 10 in. What is the maximum volume?
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